25 Nov
2020
25 Nov
'20
4:52 p.m.
On Wed, Nov 25, 2020 at 6:36 PM James Propp <jamespropp@gmail.com> wrote:
Regarding Dan’s second question, I kind of feel the answer should be 2, represented by one that joins the midpoints of the top and bottom edges and another that joins the midpoints of the left and right edges. But I’m not sure they’re genuinely different, and I don’t see why there couldn’t be other possibilities.
There are more than that. You can spiral around, connecting the top and bottom of the square as many times as you like. These represent different elements of the fundamental group, so they are not equivalent. That's enough to show that the literal answer to Dan's question is "Infinitely many", but this isn't all of them. Andy